Modern Cosmology - The Origin and Evolution of the Universe

1.0 The Cosmological Principle

The large scale structure of the universe is represented by the distribution of galaxies. Recall that gravity is an attractive force, so we expect to find clustering of galaxies. We must survey the distribution of galaxies on large-enough distance scales that gravity does not bias our results. On sufficiently large scales, the universe and the distribution of matter within it is homogeneous and isotropic.

• Homogeneous means that every region is the same as every other region.
• Isotropic means that the universe looks the same in every direction.
• "Same" means the same average density, temperature, and composition.

This requirement of a homogeneous and isotropic universe is called the cosmological principle. Note that planets and stars exist and are very localized regions of high density. Therefore, on small size scales the universe is highly inhomogeneous.

2.0 The Big Bang theory of the origin of the universe

The Big Bang describes some observations but not others. In section 2, the Standard Model will be described. Then in Section 3, a modification of the Standard Model, called the Inflationary Model of the Big Bang, will be described.

2.1 The Expanding Universe

Einstein's General Theory of Relativity predicted that the universe was not static, but was either expanding or contracting (1920). Einstein didn't believe the result because there was no evidence to support it.

Edwin Hubble was measuring the distances to distant objects, like the galaxies in the Virgo and Perseus clusters, and discovered that they are receding away from us. The velocity of recession increased with increasing distance - this observation is compatible with an expanding universe. Based on these observations he derived Hubble's Law which relates velocity with distance, v = Hd.

• v is the recessional line-of-sight velocity of the galaxy
• d is the distance to the galaxy
• H is a constant relating v and d; it lies somewhere between 50 and 100 km/s/Mpc, probably close to 65 km/s/Mpc.

Note that recessional velocities measured are only the component along the line of sight to the source. They are measured by comparing the shift of spectral line radiation from the galaxies with that of a source at rest (i.e., in the laboratory). These spectral lines are shifted to the red end of the spectrum, hence the name "redshift".

It is incorrect to think of the material inside the universe as expanding into empty space - rather, the underlying geometry of the universe is expanding, and the material inside is being carried along with it. Think of attaching pennies to the outside of a balloon, and then blowing up the balloon. The same amount of rubber always exists between two pennies, however, the physical distance between the two pennies is getting larger.

Think also of stretching a chessboard. The distance between the corners of the board is still 8 squares. However, the physical distance between the corners is increasing.

Think also of Hubble's law. If every square on the chessboard is getting larger at the same rate, X, then objects located two squares away from each other are getting farther apart at a rate 2 times X.

2.2 The Big Bang Theory

If the universe is going to be larger tomorrow, then it was smaller yesterday. It makes sense that the universe was quite tiny a long time ago, perhaps even infinitesimal in size (called a "primordial atom" by Georges Lemaitre; Lemaitre was the first person to put together Einstein's theory with Hubble's observation). Some initial event occurred that started the expansion - we call this event the Big Bang (Fred Hoyle's term of ridicule for Lemaitre's description of a "big noise"). We are still feeling the effects of the Big Bang today.

The Big Bang theory makes three predictions about the state of our present universe, eachof which was been observationally verified and are called the three classic demonstrations of the validity of the theory:

1. redshift of distant galaxies
2. cosmic background radiation
3. abundances of the elements

2.3 Redshift of galaxies

The redshift of galaxies is represented by Hubble's Law. Hubble's Law contains the parameter H (the Hubble constant), which relates v to d. It is in units of km/s/Mpc. It describes how fast the universe is expanding. Suppose the Hubble constant is 65 km/s/Mpc, then a galaxy at a distance of 1 Mpc is fleeing away from us at a speed of 65 km/s. A galaxy at a distance of 2 Mpc is fleeing away from us at a speed of 130 km/s.

The inverse of the Hubble constant is approximately the age of the universe, although this number has to be modified depending upon if the expansion is steady, accelerating or decelerating over time.

2.4 Cosmic Background Radiation

In the early universe, material would have been highly compressed. A highly compressed material will be hot, therefore the early universe was at a very high temperature. A hot substance will spontaneously emit light, in the form of blackbody radiation (recall Kirchoff's laws). As the universe expands, the temperature of this light will decrease. The existance of this light was theorized in the 1950s, and discovered in the 1960s by Penzias and Wilson. It is called the cosmic background radiation (CBR). The current spectrum of the CBR corresponds to a blackbody temperature of 2.7 kelvin (the peak of the blackbody curve is at a wavelength of about 1 millimetre). This temperature is extremely low, and can be considered to be the average temperature of the universe.

The CBR comes at us from all directions with nearly equal intensity, and is the best demonstration we have of the cosmological principle. The CBR comes to us from when the universe was only about 100,000 years old. When the universe was younger than this age, it was opaque.

2.5 Elemental Abundances

A young, hot universe will process material within it. In the same way that the super-hot cores of stars process hydrogen into helium and other elements, the early universe would have processed helium, lithium and beryllium. This process started when the universe was about 10 seconds old, and ended about 30 minutes later.

By observing large parts of the universe we have discovered that it is composed of 24% helium by mass, and about one billionth of one percent of lithium and beryllium. These abundances are strong supporting evidence for the Big Bang model.

2.6 Final remarks about the Standard Model

The Big Bang is then quite successful - it explains the recession of distant objects, the CBR, and the abundance of heavy elements. Note that ALL objects in the universe are receding from each other, however, the recession is only measurable at large distances. Note also that the expansion of the universe is not pulling objects apart. Gravitational forces are strong enough to hold together the Milky Way galaxy together against the expansion.

What has been described above is called the Standard Big Bang model.

3.0 The Shortcomings of the Big Bang Model

The Standard Big Bang model makes three classic false predictions,and hence has been revised. These shortcomings are called the horizon problem, the flatness problem, and the monopole problem. I will describe each problem, and how the Inflationary Big Bang model solves it.

3.1 The Horizon Problem

The maximum speed of travel in the universe is the speed of light. Nothing can travel faster. However, the actual geometry of the universe itself can expand at a "speed" faster than light. Think about it - suppose that both you and I can travel at 75% the speed of light. If we travel away from each other, then our relative speed is faster than light (150%). There can be no communication between us since no signal sent by you can catch up to me, and vice versa.

So, if we point our telescopes in opposite directions, we can see areas of the universe that have not been in contact with each other. Question - how can these areas be so alike? How can they have the same temperature, density, and other measurable properties? There is a law in physics that, in order for an equilibrium to be established in a system, every portion of the system has to communicate with every other portion to determine what the final state will be.

The Standard Model cannot answer this question.

3.2 The Flatness Problem

The universe has been expanding outward, but it has also been slowing down. This slowing down is due to the fact that the universe contains matter. Matter attracts itself gravitationally. This gravitational attraction acts to slow down the expansion.

The universe has three fates, depending on the balance between the Big Bang energy that propelled it outwards, and the gravitational attraction pulling it inwards. If the matter in the universe cannot slow the expansion down, then the universe will expand forever (called an "open" universe). If there is a lot of matter in the universe, then the expansion will halt, and collapse will begin (called a "closed" universe). If the expansion and contraction forces balance exactly, then the universe will halt its expansion at an infinite size (called a "critical" universe) after an infinite amount of time.

The universe is somewhere between 12 and 18 billion years old. That is enough time for the "open" or "closed" cases to have become measurable to many decimal places. The simple fact that we're here means that we live in a universe that is quite close to critical. There is no reason for this happenstance to be so - it is regarded as an arbitrary fine-tuning of the initial state of matter in the universe. The problem asks why are we so close to the critical case?

Another way to look at the problem is to realize that at early times, the three possible fates for the universe resemble each other very closely, and in fact they all resemble the critical case. As time goes by the three fates quickly distinguish themselves. In order for us to observe ourselves in a critical universe, we must assume that we are living at a special epoch. Here, "special" means a combination of unlikely, short-lived, and possibly privileged. However, a fundamental assumption of cosmology is that we do NOT live in a special place or at a special time (a statement called the "Copernican Principle" or the "Principle of Mediocrity"). Hence we have two assumptions that are mutually contradictory.

A paradox is a situation where two contradictory situations seem to co-exist. Here, we assume that our universe is not special in any way, and yet the evidence suggests that it is special. The Standard Model does not resolve the paradox.

3.3 The Monopole Problem

Certain models in particle physics predict the existence of "exotic" elementary particles, like magnetic monopoles. A monopole is a "north" magnetic charge without an accompanying "south" charge (or vice versa). So far we have only observed the two bound together. The Big Bang predicts that these particles should have been produced in sufficient quantity that we would see them today. Where are they?

Note that the exotic particles spoken of in this section are not anti-matter particles. The matter/anti-matter problem is different from the monopole problem and is not discussed in this course.

4.0 The Inflationary universe model

"Inflation" refers to a period in the early universe when the universe (or some small portion of it) accelerated its expansion, and not decelerated as predicted (by gravitation). In other words, a small portion of the universe became very large, very quickly. This portion became the universe we live in today. Such a rapid expansion solves all three problems above.

4.1 Inflation solves the three classic problems

Before inflation, the universe was small enough that all points within it could be in contact with each other, thus allowing an equilibrium to be established. Inflation speeds up the expansion to produce a universe of the size we see today. Therefore, the horizon problem is solved.

Inflation also serves to smooth out the geometry of the universe mathematically, basically by making the so-called curvature terms unimportant in deciding the "openness" or "closedness" - hence the universe can be arbitrarily close to being "critical", regardless of the amount of matter present. In other words, in an inflationary universe the amount of matter does not determine the fate of the universe. This effect solves the flatness problem.

Another way to look at the flatness problem is to recall that, at early times, the universe will appear to be at or near the critical case. If inflation can expand the universe more quickly than the curvature can change, then after inflation the universe retains its sense of "criticalness" regardless of the matter present. I have presented another way to look at how inflation solves the flatness problem.

The accelerated expansion will dilute the number of monopoles per unit volume - in other words, they become so rare that we do not expect to detect them. The monopole problem is thus solved.

4.2 How does one produce an Inflationary universe?

The question is, of course, why should the universe go through a period of accelerated expansion? The method used by theorists is to assume that the early universe had an energy associated with a vacuum. There is nothing in a vacuum, naturally, and there still isn't, except that it now has a potential energy. Potential energy is "the ability to do work", if you recall. In other words, each and every point inside the universe had an associated latent ability to perform work - a potential energy. This situation is called a "false vacuum."

A false vacuum will act like a pressure - this pressure will cause the universe to be pushed outward.

Now we have to get rid of this vacuum energy, since the universe is clearly not inflating today. This evolution of events is, in some ways, quite natural - a system always wants to move to a state of minimum energy, so the universe would try to find a way to decrease this potential energy as much as possible. Most probably, the energy was spontaneously converted into matter and radiation - as extra matter was dumped into the universe, the false vacuum was decreased to zero and the inflationary period stopped.

Theorists have tried using various models to explain how the potential energy (false vacuum) behaves. There are therefore various types of inflation - "old", "new" and "chaotic" inflation. "Old" inflation (Alan Guth, 1980) tried to capture the universe in a stable state (of non-zero energy) from which is had to escape. The theory has problems in that it produces areas in the universe where the false vacuum would remain. We don't observe this effect.

"New" inflation (A. Linde, A. Albrecht, P. Steinhardt) is simpler, and describes a gentle decline from a non-zero energy state (false vacuum) to what we see today (true vacuum).

"Chaotic" inflation (Linde) is a way for separate parts of the universe to have their vacuum energy experience a non-gentle decline to zero - there would be fluctuations back up to higher values, thus leading to parts of the universe that would inflate for longer, and no longer have any contact with other parts of the universe. You therefore get multi-verses. In other words, you get a universe with a fractal geometry.

4.3 How does Inflation relate to the scientific method?

The concept of inflation was constructed specifically to solve the problems associated with the Big Bang model. A result of this construction is that inflation cannot be tested, and as such it cannot be subjected to the scientific method. Inflation is therefore not a proper theory, and some researchers consider the whole idea to be a pipe dream.

Inflation is not without merit. It is a relatively simple modification to the Big Bang model that eliminates the three classic problems simultaneously, which is the power behind it.

5.0 The Accelerating Universe

The results and theories explained above summarizes several decades of observational and theoretical work, ending at about the turn of the previous century. Observers were concentrating on working out some of the unknown numbers in the models.

In particular, we expect the expansion of the universe to be slowed somewhat by the gravitational "resistance" of the matter in the universe. This slowdown in the expansion of the universe is called "deceleration". Serious efforts were made to try to observe galaxies very far away to try to discover the rate of deceleration. It was expected that, ss the universe expands, the distance between objects increases and therefore the force of gravity acting to decelerate the universe would get weaker.

The most modern observations discovered a surprising result, that the universe is accelerating, and not decelerating! An accelerating universe suggests that there is a repulsive force about which we have no knowledge.

The concept of a repulsive force is not a new one. Einstein himself considered it when trying to reconcile his theory of a dynamic universe with the pre-Hubble observations of a static universe. Einstein represented this force using an uppercase Greek Lambda. This Lambda is called the Cosmological Constant, and current talk about our universe refer to it as being Lambda-dominated.

Mathematical models of a Lambda-dominatd universe predict that this repulsive force will get stronger as the universe gets larger, in direct contrast to gravity (so calling Lambda an anti-gravity force would be incorrect).

The existence of a Cosmological Constant also makes other predictions. One prediction is that the universe will expand so quickly that distant objects that we can see today will eventually be receding from us at greater than light speed, so that they will disappear from our view. Any object located in a part of the universe that is receding away from us at light speed or greater is said to be outside our horizon. Our viewable universe will become smaller over time as our horizon approaches us.